An efficient quantum algorithm for colored Jones polynomials

Details An efficient quantum algorithm for colored Jones polynomials An efficient quantum algorithm for colored Jones polynomials

2006-06-20

arxiv.org/abs/quant-ph/0606167v1

Physics

Quantum Physics

9 pages, 5 figures

Scientific paper

We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. Our construction is based on SU(2) Chern-Simons topological quantum field theory (and associated Wess-Zumino-Witten conformal field theory) and exploits the q-deformed spin network as computational background. As proved in (S. Garnerone, A. Marzuoli, M. Rasetti, quant-ph/0601169), the colored Jones polynomial can be evaluated in a number of elementary steps, bounded from above by a linear function of the number of crossings of the link, and polynomially bounded with respect to the number of link strands. Here we show that the Kaul unitary representation of colored oriented braids used there can be efficiently approximated on a standard quantum circuit.

Affiliated with

Also associated with

No associations

Rating

An efficient quantum algorithm for colored Jones polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An efficient quantum algorithm for colored Jones polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An efficient quantum algorithm for colored Jones polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40596